A. Benseghir, W. A. T. Wan Abdullah, B. B. Baizakov, and F. Kh. Abdullaev, Matter-wave soliton bouncing on a reflecting surface under the effect of gravity, physical review a 90, 023607 (2014)

The dynamics of a matter-wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The analytical description is based on the variational approach. Resonant oscillations of the soliton’s center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential, are analyzed. In numerical experiments we observe the Fermi-type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared to the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.